Today, computer aided engineering (CAE) has been used for supporting engineers in tasks such as analysis, simulation, design, manufacture, etc. In a conventional engineering design procedure, CAE analysis (e.g., finite element analysis (FEA), finite difference analysis, meshless analysis, computational fluid dynamics (CFD) analysis, modal analysis for reducing noise-vibration-harshness (NVH), etc.) has been employed to evaluate responses (e.g., stresses, displacements, etc.). Using automobile design as an example, a particular version or design of a car is analyzed using FEA to obtain the responses due to certain loading conditions. Engineers will then try to improve the car design by modifying certain parameters or design variables (e.g., thickness of the steel shell, locations of the frames, etc.) based on specific objectives and constraints. Another FEA is conducted to reflect these changes until a “best” design has been achieved. However, this approach generally depends on knowledge of the engineers or based on a trial-or-error method.
Furthermore, as often in any engineering problems or projects, these objectives and constraints are generally in conflict and interact with one another and design variables in nonlinear manners. Thus, it is not very clear how to modify them to achieve the “best” design or trade-off. This situation becomes even more complex in a multi-discipline optimization that requires several different CAE analyses (e.g., FEA, CFD and NVH) to meet a set of conflicting objectives. To solve this problem, a systematic approach to identify the “best” design, referred to as design optimization, is used.
Optimization of such systems with more than one design objective functions is referred to as multi-objective optimization. Contrary to the single-objective optimization problems, the multi-objective optimization problems do not yield a single optimum solution. Instead, it results in a set of optimal solutions that represent different trade-offs among design objectives. These solutions are referred to as Pareto optimal solutions or Pareto optimal solution set. Design objective function space representation of the Pareto optimal solution set is known as Pareto optimal front or frontier (POF).
One of the problems for obtaining POF in multi-objective design optimization is the requirement of having a large number of experiments (i.e., unique design alternatives in the design space), which can be very expensive in terms of time and/or computing costs.
It would, therefore, be desirable to have methods and systems for efficiently selecting design alternatives in a multi-objective design optimization of a product.